U = 3log(7) v +10 - Sketch the graph of the Logarithmic Function

The (7) being base 7. Someone please shed some light on this :D

In the real number system log(7) v is only defined for positive values of v so restrict your graph to positive values of v.

log(7)1 = 0 so when v = 1, u = 10.

For large values of v, us is large and positive.

For very small values of v, log(7) v is a big negative number.

To find the v-intercept, set u =0.
0 = 3log(7)v + 10
3log(7)v = -10
log(7)v = -10/3
v = 7^(-10/3) . . . a very small positive number.

u = 3ln v / ln 7 + 10 so du/dv = 3 / (vln7).
So for positive values of v the gradient is always positive but as v increases the gradient decreases.

Combine all the above and you should have a good sketch.